Is prayer to be shortened only in area (B), or only in area (A), or is prayer not to be shortened throughout the entire duration of travel, when dividing the travel period (15 days) between two areas (A) and (B) and returning to area (A) before the final departure?

If a traveler intends to stay in a country for four days or more, their journey is considered terminated, and they are not permitted to avail themselves of the concessions of travel, such as shortening prayers (qasr) or combining them (jam'). This is the view of the majority of scholars, and it is the opinion of 'Uthman ibn 'Affan, Malik, Al-Shafi'i, and Ahmad in the more authoritative of his two narrations. Therefore, if your stay in Area (A) is eight days, you are not entitled to shorten or combine prayers. As for your stay in Area (B), if it is four days or more, you are considered a resident; if it is less than that, you are considered a traveler. If you return to Area (A) and stay there for four days, you are considered a resident; if less, you are a traveler. Shaykh al-Islam Ibn Taymiyyah held the view that a traveler may shorten prayers as long as they do not intend an indefinite stay, and this is the view preferred by Shaykh Ibn 'Uthaymeen. A journey is considered terminated upon a person's arrival at their homeland or at a place where they have a consummated wife.